Based on a new self-consistent outer gap model, we
statistically study luminosity properties of γ-ray pulsars
with ages of ≤ yr in the Galaxy as well as
those with ages of ≤ yr in the Gould belt using
a Monte Carlo method, where the γ-ray beaming effect has
been included. Generally, the relation between γ-ray
luminosity, , and pulsar spin-down power, Lsd,
can be expressed as , where
δ is a parameter that depends on the galactic latitude and
the γ-ray threshold. For a given γ-ray threshold
(for example, the EGRET threshold or GLAST threshold), the
parameter δ is an increasing function of the galactic
latitude. For the EGRET threshold, δ changes smoothly with
the galactic latitude. For the GLAST threshold, however, δ
has a minimum at , and δ
increases by a factor of ~2 at the range of relative to δ at , and then increases smoothly as the galactic latitude
further increases. The reason for this is that high galactic
latitude γ-ray pulsars are dominated by mature pulsars. In
fact, the ratio of γ-ray pulsars with their ages of >106 yr to all simulated γ-ray pulsars also increases with the
galactic latitude. For the γ-ray pulsars produced in a
fixed range of galactic latitude, the parameter δ increases
slightly with the sensitivity of γ-ray detector.

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